LMPO

Execution Time (secs)	0.034
Answer	MAYBE
Input	TCT 09 ma1

MAYBE

We consider the following Problem:

  Strict Trs:
    {  f(s(x), y) -> f(x, g(x, y))
     , f(0(), y) -> y
     , g(x, y) -> y}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.026
Answer	MAYBE
Input	TCT 09 ma1

MAYBE

We consider the following Problem:

  Strict Trs:
    {  f(s(x), y) -> f(x, g(x, y))
     , f(0(), y) -> y
     , g(x, y) -> y}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.024
Answer	MAYBE
Input	TCT 09 ma1

MAYBE

We consider the following Problem:

  Strict Trs:
    {  f(s(x), y) -> f(x, g(x, y))
     , f(0(), y) -> y
     , g(x, y) -> y}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.040
Answer	YES(?,POLY)
Input	TCT 09 ma1

YES(?,POLY)

We consider the following Problem:

  Strict Trs:
    {  f(s(x), y) -> f(x, g(x, y))
     , f(0(), y) -> y
     , g(x, y) -> y}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,POLY)

Proof:
  The input was oriented with the instance of
  Polynomial Path Order (PS) as induced by the safe mapping

   safe(f) = {2}, safe(s) = {1}, safe(g) = {1, 2}, safe(0) = {}

  and precedence

   f > g .

  Following symbols are considered recursive:

   {f, g}

  The recursion depth is 2 .

  For your convenience, here are the oriented rules in predicative
  notation (possibly applying argument filtering):

   Strict DPs: {}
   Weak DPs  : {}
   Strict Trs:
     {  f(s(; x); y) -> f(x; g(; x, y))
      , f(0(); y) -> y
      , g(; x, y) -> y}
   Weak Trs  : {}

Hurray, we answered YES(?,POLY)

Small POP*

Execution Time (secs)	0.025
Answer	MAYBE
Input	TCT 09 ma1

MAYBE

We consider the following Problem:

  Strict Trs:
    {  f(s(x), y) -> f(x, g(x, y))
     , f(0(), y) -> y
     , g(x, y) -> y}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.066
Answer	YES(?,O(n^1))
Input	TCT 09 ma1

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(s(x), y) -> f(x, g(x, y))
     , f(0(), y) -> y
     , g(x, y) -> y}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,O(n^1))

Proof:
  The input was oriented with the instance of
  Small Polynomial Path Order (WSC,
                             PS,
                             Nat 1-bounded) as induced by the safe mapping

   safe(f) = {2}, safe(s) = {1}, safe(g) = {2}, safe(0) = {}

  and precedence

   f > g .

  Following symbols are considered recursive:

   {f}

  The recursion depth is 1 .

  For your convenience, here are the oriented rules in predicative
  notation (possibly applying argument filtering):

   Strict DPs: {}
   Weak DPs  : {}
   Strict Trs:
     {  f(s(; x); y) -> f(x; g(x; y))
      , f(0(); y) -> y
      , g(x; y) -> y}
   Weak Trs  : {}

Hurray, we answered YES(?,O(n^1))

Problem TCT 09 ma1

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)